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<p>The following graphs show <b>comparisons between calculated and
measured mean ionic activity coeficients</b> at <nobr>25&deg;C.</nobr></p>

<p><b>1:1 electrolytes:</b>
measured <nobr>&#947;<sub>&plusmn;</sub></nobr> data at
<nobr>25&deg;C</nobr> for NaCl compared with results obtained using both the Davies eqn.
and the eqns. by Helgeson <nobr><i>et al</i>.:</nobr></p>
<p>
<center>
<img src="images/log_gamma_1-1.gif" alt="log_gamma_1:1" title="log_gamma_1:1" height="240" width="300" border="1">
</center>
</p>
<p class="cont">
Note that the Davies eqn. should not be used for ionic strengths
<nobr>&gt; 0.1 M.</nobr> It should also be noted that the paramaters for the eqns.
by Helgeson <nobr><i>et al</i>.</nobr> were chosen to fit the NaCl data over
a wide range of temperatures and concentrations. It is <i>not</i> surprising that
the model fits the data so well. 
</p>

<p><b>1:2 and 2:1 electrolytes:</b>
<nobr>&#947;<sub>&plusmn;</sub></nobr> data at
<nobr>25&deg;C</nobr> for <nobr>CaCl<sub>2</sub></nobr> and
<nobr>Na<sub>2</sub>SO<sub>4</sub></nobr> compared with results obtained using both
the Davies eqn. and the eqns. by Helgeson <nobr><i>et al</i>.:</nobr></p>
<p>
<center>
<img src="images/log_gamma_1-2.gif" alt="log_gamma_1:2" title="log_gamma_1:2" height="240" width="300" border="1">
</center>
</p>
<p class="cont">
Note that the mean activity coefficients for an unsymmetric electrolyte
X<sub>&nu;<sub>X</sub></sub>Y<sub>&nu;<sub>Y</sub></sub> is:</p>
<p class="indent">
<nobr>&#947;<sub>&plusmn;</sub><sup>&nu;</sup></nobr> =
<nobr>
&#947;<sub>X</sub><sup>&nu;<sub>X</sub></sup>
&#947;<sub>Y</sub><sup>&nu;<sub>Y</sub></sup>
</nobr>
</p>
<p>For a <nobr>1:2</nobr>
<nobr>(or 2:1)</nobr> electrolyte,
for example <nobr>CaCl<sub>2</sub>:</nobr></p>
<p class="indent">
<nobr>&#947;<sub>&plusmn;</sub><sup>3</sup></nobr> =
<nobr>
&#947;<sub>Ca<sup>2+</sup></sub>
&#947;<sub>Cl<sup>&#8722;</sup></sub><sup>2</sup>
</nobr>
</p>
<p class="cont">and</p>
<p class="indent">
<nobr>log &#947;<sub>&plusmn;</sub>(CaCl<sub>2</sub>)</nobr> =
<nobr>(log &#947;<sub>Ca<sup>2+</sup></sub></nobr>
<nobr>+ 2 log &#947;<sub>Cl<sup>&#8722;</sup></sub>)&nbsp;/&nbsp;3.</nobr>
</p>

<p><hr> <!-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - --></p>

<p><b>Higher Concentrations:</b> the performance of these equations deteriorates
quickly above <nobr><i><b>I</b></i> &#8776; 0.3M:</nobr>
<p>
<center>
<img src="images/log_gamma_1-1b.gif" alt="log_gamma_1-1 high conc." title="log_gamma_1-1 high conc." height="240" width="300" border="1">
</center>
</p>
<p>
<center>
<img src="images/log_gamma_1-2b.gif" alt="log_gamma_1-2 high conc." title="log_gamma_1-2 high conc." height="240" width="300" border="1">
</center>
</p>
</p>

<p><hr> <!-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - --></p>

<p>
The experimental <nobr>&#947;<sub>&plusmn;</sub></nobr> data for NaCl, <nobr>CaCl<sub>2</sub></nobr> and
<nobr>Na<sub>2</sub>SO<sub>4</sub></nobr> may be found in the appendices of:
</p>
<p class="indent">
<nobr>R.A. Robinson</nobr> and <nobr>R.H. Stokes</nobr> (1970)
<i>Electrolyte Solutions</i>, <nobr>2<i>nd</i> edn.,</nobr> London: Butterworth
&amp; <nobr>Co.,</nobr> <nobr>571 pp.</nobr>
(reprinted in 2002 by Dover Publications, <nobr>Inc.,</nobr> USA). 
</p>

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